Marcus Stewart's deftly taken goal just before half-time settled the match, but Sunderland had to survive a second-half onslaught by the Blades.
The Wearsiders stood strong and with Ipswich and Wigan both only drawing, Mick McCarthy's men stayed third but moved within three points of top spot.
There was no sign of the crescendo that was to build in an opening 20 minutes, when two hard-working and committed sides cancelled each other out. It was all huff and puff in midfield, with neither goalkeeper stretched.
The one shining light in it all was Stewart. The experienced forward was sly as a fox with his movement, coming deep to gather possession for his side and then darting in behind a defence that was having trouble keeping close to him.
United had the first effort of note after ten minutes, but Chris Morgan could not get enough on his header from a long throw and home keeper Thomas Myhre saved easily.
Sunderland responded immediately as Stewart and Elliott combined well for the first time - Stewart feeding his striker partner in the box but Stephen Elliott could not beat Blades goalkeeper Paddy Kenny from a narrow angle.
Stewart then released Elliott for a clear run on goal, but the Irishman was unlucky to see his brilliant chip leave Kenny stranded, only to come back off the bar.
Stewart then flashed across the face of goal as Sunderland took a stranglehold on the match.
The goal eventually came with only a minute of the half remaining and it was no surprise that Stewart was the man to score.
Elliott beat Leigh Bromby on the left and fired over a cross that Dean Whitehead just failed to connect with, before Stewart guided a superbly controlled left-foot volley past the helpless Kenny.
United had to improve after the break, and that they did with a second-half of almost relentless pressure.
Andy Gray went close to a leveller before the game threatened to boil over when Julio Arca was spoken to by the referee for a two-footed tackle.
Danny Cullip mis-kicked in front of goal when Alan Quinn's corner fell to him in the 62nd minute, but Gray was more accurate when he got free inside the area moments later, only to be denied by a brilliant stop from Myhre.
With 15 minutes to go, Blades were once again left wondering how they were not level when substitute Jonathon Forte lashed a left-foot drive towards the top corner, but Myhre rose acrobatically to push the ball away.
Black Cats substitute Chris Brown was denied by a stunning double save from Kenny ten minutes from time, but a second goal would have been harsh on the visitors.
United threw men forward and deep into added time even sent Kenny up for a corner, but there was no way through.